Emotions as infectious diseases in a large social network: the SISa. model

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1 1 2 Emotions as infectious diseases in a large social network: the SISa model 3 4 Alison L. Hill, David G. Rand, Martin A. Nowak, Nicholas A. Christakis June 6, Supplementary Material Framingham Heart Study Dataset In this study, we evaluate the assumption that emotions behave like infectious agents. We use data from the Framingham Heart Study (Dawber, 1980) and the framework discussed above to test whether positive and negative emotions fit the dynamics of an infectious disease. The Framingham study was initiated in 1948 in Framingham, Massachusetts and has continued enrolling subjects through the present. We examined individuals in the Offspring Cohort, enrolled starting in Subjects come to a central facility at regular intervals (approximately every 3 years) for medical examination and collection of other survey data. In additional to information on mental and physical health, subjects were asked to name at least one close friend at each exam, and were also connected to all first-order relatives, coworkers, and residential neighbours For each subject, the following social connection data is available: (i) each other person to whom they were connected, (ii) the dates of initiation and termination of that relationship, (iii) the type of relationship (neighbour, coworker, first-degree relative, or friend), and (v) the geographic distance between the two subjects. The social network for each exam was constructed by creating a network matrix G, where G ijk = 1 if subject i nominated subject j as a connection before or during the time that subject i was administered exam k. All relationship types are mutual except for friendships, which are self-nominated, such that G ijk G jik is possible for friendships. 23 1

2 Individuals in the Framingham Heart Study were administered a widely validated psycho-social exam called the CES-D (The Center for Epidemiologic Studies Depression Scale, (Radloff, 1977)) atexams6and 7 (administered on average in 1997 and 2000). The full version of this survey style exam is commonly used to classify depressive symptoms (Rush, 2007; Radloff, 1977; Schroevers et al., 2000) and a subscale which comprises a distinct factor (Thorson and Powell, 1993; Joseph and Lewis, 1995; Pressman and Cohen, 2005; Radloff and Teri, 1986; Sheehan et al., 1995) has also been validated as a measure of positive affect (Moskowitz, 2003; Ostir et al., 2000; Pressman and Cohen, 2005). Similar measures of positive affect using subjective surveys have been shown to be highly correlated with objective measures of well-being (Oswald and Wu, 2010). We have chosen to call this positive state measured by the CES-D content, though it has been called happiness by others. It is also related to optimism and self-esteem. The negative emotion measured by the full CES-D scale is generally called depression, though as described in (Rush, 2007), this measure is generally agreed to represent a long-term emotional state of depressive symptomology that is distinct from (and less severe than) the mental illness state of clinical depression. To prevent confusion, we have called this measure discontent throughout the paper A content score and a discontent score were calculated for each subject from the raw responses to 20 multiple choice questions from the CES-D. The questions asked subjects to judge the frequency with which they experienced a particular feeling or behaviour, with available answers being 0=(rarely or none of the time, <1 day per week), 1=(some or a little of the time, 1-2 days per week), 2=(occasionally or a moderate amount of the time, 3-4 days per week) and 3=(most of the time, 5-7 days per week). Subjects are classified as content if they scored the maximum value of 3 on each of four particular questions related to positive feelings. Summing the answers to the 16 CES-D questions related to negative feelings and adding inverted answers to the 4 positive questions, subjects are classified as discontent if they have a total score greater than 16 (out of a possible 60). Individuals who are neither content nor discontent are classified as neutral. The distribution of emotional states among our subjects is shown in Figure S1A. We find that less than 1 out of every 1000 subjects are both content and discontent, validating our classification of emotions into the three states content, discontent and neutral. Figure S2B shows the number of people who made each transition between the two examinations. 52 2

3 Neutral Content Not Content Discontent Not Discontent 915 Content Discontent 71 (a) (b) Figure S1. A) The distribution of subjects between four emotional states measured by the CES-D. Subjects were classified as first as either content or not content, and then separately as discontent or not discontent. Individuals who are neither content nor discontent are classified as neutral. As expected, very few people who are classified as content are also classified as discontent, while those that are not content may be discontent or not discontent. Fraction content=0.63, discontent=0.09, neutral=0.28. B) Each circle represents an emotional state, and the arrows and numbers display the number of transitions that occurred between each state Super-infection: Direct transitions between content and discontent infected states Figure S1B shows that direct transitions between the content and discontent states are sometimes observed. There are two possibles explanations for these transitions. Firstly, because exams are only every 3 years, it is possible that some of these individuals actually moved through the neutral state, and thus made two transitions between observations (ie content to neutral to discontent). The second explanation is that these individuals actually moved directly between these states via super-infection. We can predict how often we would expect double transitions to occur within the 3 year window, based on the estimates for each individual transition. These predictions are lower than the observed number of direct transitions. Thus the difference between the observed and expected can be interpreted as the rate of actual direct transitions. This is explained in detail below. The estimated rates of all transitions are visualized in Figure 3 in the main text For a Markov process, if an event occurs at a rate a, then the probability that this event has occurred after a time t is 1 e a t.iftwoeventsoccuratratesa 1 and a 2, and must occur in that sequential order, then in a time period t the probability that both occur is : 67 t 0 a 1 (1 e a2( t t) ) dt = a 1 t a 1 a 2 (1 e a2 t ) (1) 3

4 Content Discontent A Regression Slope=0.035 (p=0.071) Intercept= Discontent Contacts B Discontent Content Regression Slope= (p=0.945) Intercept= Content Contacts Figure S2. Observed rates of direct transitions between content and discontent and vice versa. We see no significant dependance on the number of infected contacts for these direct transitions From this expression we can calculate the expected rate of double transitions between content and dis- content (going through the neutral state) in a single time period between exams For content discontent, the two transitions that must occur are : content to neutral (a 1 = g c )and neutral to discontent (a 2 = a d + β d n d ). There values are: g c =0.088 ± /year 75 a d =0.040 ± /year 76 β d =0.04 ± 0.02 /year For discontent content, the two transitions that must occur are : discontent to neutral (a 1 = g d )and neutral to content (a 2 = a c + β c n c ). There values are: g d =0.13 ± 0.02 /year 81 a c =0.18 ± 0.01 /year 82 β c =0.02 ± 0.01 /year 4

5 83 Using Equation 1, the expected rate of double transitions are (with standard deviations included): content to discontent: c expected =(0.004 ± 0.001) + (0.004 ± 0.001) n d /year 86 discontent to content: c expected =(0.025 ± 0.004) + (0.003 ± 0.002) n c /year 87 Observed double transition, from Figure S2: content to discontent: c observed =(0.013 ± 0.002) + (0.014 ± 0.019) n d /year 90 discontent to content: c observed =(0.097 ± 0.016) + ( ± 0.043) n c /year Note that the contact dependent terms for the double transition are observed to be non-significant, and also expected to be overlapping with zero due to the margins of error on the calculated rates. We hence ignore them for the reported rates of double transitions. The rate of direct bypass transitions is the extra number of transitions that cannot be accounted for by double transitions. This is found by subtracting the expected rates (c expected )fromtheobservedrates(c observed ) Rate of direct bypass transition: content to discontent: s cd =(0.009 ± 0.003) /year 100 discontent to content: s dc =(0.07 ± 0.02) /year It is interesting to note that in Figure S1B, the number of individuals transitioning directly from content to discontent is very similar to number transitioning from discontent to content. The same is true of the transitions between content and neutral, and between discontent and neutral. Thus the system is in detailed balance, suggesting a unique subset of the population may be responsible for the direct transitions between content and discontent. For example, it could be those suffering from bipolar disease, who represent about 1% of the population and switch between manic and discontent episodes on the order of months

6 108 References Dawber, T. R. (1980). The Framingham study: the epidemiology of atherosclerotic disease. Harvard Univer- sity Press, Cambridge Joseph, S. and Lewis, C. A. (1995). Factor analysis of the center for epidemiological Studies-Depression scale. Psychological reports, 76: Moskowitz, J. T. (2003). Positive affect predicts lower risk of AIDS mortality. Psychosom Med, 65(4): Ostir, G. V., Markides, K. S., Black, S. A., and Goodwin, J. S. (2000). Emotional well-being predicts subsequent functional independence and survival. Journal of the American Geriatrics Society, 48(5): PMID: Oswald, A. J. and Wu, S. (2010). Objective confirmation of subjective measures of human Well-Being: 118 evidence from the U.S.A. Science, 327(5965): Pressman, S. D. and Cohen, S. (2005). Does positive affect influence health? Psychological Bulletin, 131(6): Radloff, L. S. (1977). The CES-D scale: A self-report depression scale for research in the general population. Applied psychological measurement, 1(3): Radloff, L. S. and Teri, L. (1986). Use of the center for epidemiological Studies-Depression scale with older adults. Clinical Gerontologist, 5(1): Rush, A. J. (2007). Handbook of psychiatric measures. Amer Psychiatric Pub Inc Schroevers, M., Sanderman, R., van Sonderen, E., and Ranchor, A. (2000). The evaluation of the center for epidemiologic studies depression (CES-D) scale: Depressed and positive affect in cancer patients and healthy reference subjects. Quality of Life Research, 9(9): Sheehan, T. J., Fifield, J., Reisine, S., and Tennen, H. (1995). The measurement structure of the center for epidemiologic studies depression scale. Journal of Personality Assessment, 64(3): Thorson, J. A. and Powell, F. C. (1993). The CES-D: four or five factors? Society, 31(6): Bulletin of the Psychonomic 6

7 CES-D Questions. Questions #4, 8, 12 and 16 were used to construct the content scale. 1. I was bothered by things that don't usually bother me. Most or all of the time (5-7 days) 2. I did not feel like eating; my appetite was poor. Most or all of the time (5-7 days) 3. I felt that I could not shake off the blues even with the help of my family or friends. Most or all of the time (5-7 days) 4. I felt that I was just as good as other people. Most or all of the time (5-7 days) 5. I had trouble keeping my mind on what I was doing. Most or all of the time (5-7 days) 6. I felt depressed. Most or all of the time (5-7 days) 7. I felt everything I did was an effort. Most or all of the time (5-7 days)

8 8. I felt hopeful about the future. Most or all of the time (5-7 days) 9. I thought my life had been a failure. Most or all of the time (5-7 days) 10. I felt fearful. Most or all of the time (5-7 days) 11. My sleep was restless. Most or all of the time (5-7 days) 12. I was happy. Most or all of the time (5-7 days) 13. I talked less than usual. Most or all of the time (5-7 days) 14. I felt lonely. Most or all of the time (5-7 days)

9 15. People were unfriendly. Most or all of the time (5-7 days) 16. I enjoyed life. Most or all of the time (5-7 days) 17. I had crying spells. Most or all of the time (5-7 days) 18. I felt sad. Most or all of the time (5-7 days) 19. I felt that people disliked me. Most or all of the time (5-7 days) 20. I could not get "going". Most or all of the time (5-7 days) Scoring for All Except Questions 4, 8, 12, and 16: 0 points Rarely or none of the time (< 1 day) 1 point 2 points 3 points Most or all of the time (5-7 days) For questions 4, 8, 12, and 16, the scoring is exactly the same except that it is reversed: "Most or all of the time" is scored 0 points, "Rarely or none of the time" is scored 3 points, etc.

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